Photo Popup is a US$0.99 app for iPhone that helps you separate an item in a photo from the background, letting you add a drop shadow, and even blur the background to bring attention to the subject.
Photographers have been doing this kind of work in Photoshop for years, but here's a way to do it in iOS.
You start by either shooting a photo or selecting one from your camera roll. With a masking tool, you cover the item by drawing on screen. Your selection turns red. If you make a mistake, there is an "undo" command that will take you to back to your first finger stroke if you need it. If you want to fine-tune the mask, you can use the unmask tool. To make the mask easier to draw, you can magnify your photo using two fingers. The virtual paint brush size stays the same, but as the picture enlarges, you can work in smaller areas.
When you are done, you can preview the image, blur the background or reduce the saturation, then create a shadow with control over direction, offset, size and blur. Your finished photo can be saved out to your photo library, or emailed.
Using the app is simple enough, and there is a built-in video tutorial. My only issue is that the brush should be offset from where your finger is so you can see where you are painting. This is a common issue with iOS apps that use a brush. On a Mac, there is no problem because you can see your brush on screen while you manipulate a mouse or trackpad. On iOS, your finger covers the very area you need to see.
If you are careful, and zoom in quite a bit, you can draw an accurate mask, and then apply a drop shadow or work on the background.
I looked at a similar app last summer called tadaa. It cost a little more, but I thought it provided better control when creating a mask.
Photo Popup requires iOS 6 or later, and is optimized for the iPhone 5, but is not universal.